I too, first saw this back in '98, and to me it was awesome. At that point I hadn't started re-watching the Showa movies in their entirety, and it had been a while since I'd seen an "all-new" Godzilla, so this was a pretty big deal to me.
I just re-watched this last night. Though my general opinion of the series as a whole is low, I thoroughly enjoyed this. Nostalgia may be partly responsible, but the film, to me, is very entertaining. The idea of exploring Godzilla's origins is neat, the build-up to the appearance of the title kaiju works well, and when Godzilla himself does finally show, he attacks Japan relentlessly! Plus, he looks plain awesome here.
True, Suzuki's effects start to visibly deteriorate, but there are some great shots in the bunch, and as a whole the effects are wild and colorful.
...Oh, and Yoshio Tsuchiya is awesome as Shindo. Really the only good role from a Toho veteran in the whole Heisei series. I think in "Bringing Godzilla Down to Size" Tsuchiya actually confesses that this was his favorite role.
As a whole: The last of the "good" Heisei movies. MechaGodzilla II had a decent story, but King Ghidorah was the last solidly entertaining movie of the '90s. Things went downhill fast.
"Vishnu takes on his multi-armed form, and says, "RAAAAAHHHOOO!!!'"